particles.variance_mcmc

MCMC variance estimators.

Author: Hai-Dang Dau

Various estimators of the asymptotic variance of a MCMC kernel, based on M chains of length P:

• initial sequence estimator of Geyer

• Tukey-Hanning

This may be used to estimate the (asymptotic) variance of estimates generated by waste-free SMC.

Functions

MCMC_Tukey_Hanning(X[, method, bias, ...])	MCMC Variance estimator using spectral variance method with Tukey_Hanning window.
MCMC_init_seq(X[, method, bias])	initial sequence estimator, see Practical MCMC (Geyer 1992) Let c_0, c_1, .
MCMC_variance(X, method)	param X: a (P, M) numpy array which contains M MCMC chains of lengths P
MCMC_variance_naive(X)
MCMC_variance_weighted(X, W, method)	Like MCMC_variance, but each column of X has a weight W that sums to 1.
autocovariance(X, order[, mu, bias])
autocovariance_fft_multiple(X[, mu, bias])	param X: numpy array of shape (P,M), which corresponds typically to M MCMC runs of length P each.
autocovariance_fft_single(x[, mu, bias])	param x: numpy array of shape (n,)
default_collector(ls)

Classes

AutoCovarianceCalculator(X[, method, bias])

An artificial device to efficiently calculate the autocovariances based on (possibly) multiple runs of an MCMC method.